I have inherited a Sun ONe 6.1 web server, and need to get patches for it. To download patches Oracle requires me to provide them with the serial number of the CD, the CD has been misplaced, I am assuming that at some point the serial number was manually entered in the system the web server is running on. Is there a way to retrieve that information?

The product does not have a serial number, maybe your CD had one but it is not linked to the binaries. If there was some number, it is purely paper based, ie linked to your license when you bought it, but the product itself does not enforce or contain this information.